Inequalities and Quantum Entanglement

From the Cauchy-Schwarz Inequality to Non-linear Entanglement Witnesses

Bachelor thesis (2019)

Authors

S.M. Loor Electrical Engineering, Mathematics and Computer Science

Contributors

J. Vermeer Analysis - EEMCS (mentor)
D. Elkouss Coronas Quantum Information and Software - EEMCS (mentor)
Cornelis Vuik Numerical Analysis - EEMCS (graduation committee member)
T.H. Taminiau QID/Taminiau Lab - QuTech Advanced Research Centre (graduation committee member)
Faculty
Electrical Engineering, Mathematics and Computer Science, Electrical Engineering, Mathematics and Computer Science
Copyright: © 2019 Stephan Loor
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Published Date

31-07-2019

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

In this thesis, two topics are studied: mathematical inequalities and non-linear quantum entanglement witnesses. First, various inequalities, like the Cauchy-Schwarz inequality (on finite dimensional vector spaces) and Jensen's inequality, along with their extensions and generalisations, are proved and discussed. The intimate relationship between these inequalities is studied. Because this thesis was restricted to finite dimensional vector spaces, the consequences of generalising the results to infinite dimensional vector spaces are finally determined. Secondly, the topic of entanglement detection is discussed - specifically, non-linear entanglement witnesses are considered. A bipartite and multipartite entanglement criterion based on the previously discussed inequalities are introduced and assessed extensively by considering their optimality, how they relate to other criteria as well as their limitations.